Bulletin    1 

Structural  Materials  Research  Laboratory 

Lewis  Institute 

Chicago 


Design  of  Concrete  Mixtures 


By 
DUFF  A.  ABRAMS 

Professor  in  Charge  of  Laboratory 


Published  by  the 

STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 

Lewis  Institute 

Chicago 

MAY,  1919 


RESEARCHES  in  the  properties  of  concrete  and  concrete  materials  at 
the  Structural  Materials  Research  Laboratory  are  being  carried  out 
through  the  cooperation  of  the  Lewis  Institute  and  the  Portland  Cement 
Association,   Chicago.     The  research  work  has  been  under  way  since 
September  1,  1914. 

The  control  of  the  policies  of  the  Laboratory  is  vested  in  an  Advisory 
Committee,  consisting  of  representatives  of  the  Lewis  Institute  and  the 
Portland  Cement  Association  as  follows : 

Lewis  Institute: 

DUFF  A.  ABRAMS,  Professor  in  Charge  of  Laboratory 
PHILIP  B.  WOODWORTH,   Professor  of  Engineering 

Portland  Cement  Association: 

F.  W.  KELLEY,  Chairman,  Technical  Problems  Committee,  Albany,  N.  Y. 
ERNEST  ASHTON,  Member,  Technical  Problems  Committee,  Allentown, 
Pa. 

The  investigations  are  being  carried  out  by  a  staff  of  engineers,  chem- 
ists, and  assistants  who  give  their  entire  time  to  this  work.  The  results 
of  these  researches  are  aiibllsEeJd  5n  the  form  of  papers  before  engineering 
and  technycaj  .societies,,  and  .in  Circulars  and  Bulletins  issued  by  the 
Laboratory!-. ;  ;-"•  "••;  •.•'"::.,:  /•**.  •..* 


DESIGN  OF  CONCRETE  MIXTURES* 

BY  DUFF  A.  ABRAMS 

,  PROFESSOR  IN  CHARGE  OF  LABORATORY 

The  design  of  concrete  mixtures  is  a  subject  of  vital  interest  to  all  engineers 
and  constructors  who  have  to  do  with  concrete  work.  The  problem  involved  may 
be  one  of  the  following : 

1.  What  mix  is  necessary  to  produce  concrete  of  proper  strength  for  a  given 

work? 

2.  With  given  materials  what  proportions  will  give  the  best  concrete  at  min- 

imum cost? 

3.  With  different  lots  of  materials  of  different  characteristics  which  is  best 

suited  for  the  purpose? 

4.  What  is  the  effect  on  strength  of  concrete  from  changes  in  mix,  consistency 

or  size  and  grading  of  aggregate  ? 

Proportioning  concrete  frequently  involves  selection  of  materials  as  well  as 
their  combination.  In  general,  the  question  of  relative  costs  is  also  present. 

The  term  "Design"  is  used  in  the  title  of  this  article  as  distinguished  from 
"proportioning"  since  it  is  the  intention  to  imply  that  each  element  of  the  problem 
is  approached  with  a  deliberate  purpose  in  view  which  is  guided  by  a  rational  method 
of  accomplishment. 

The  design  of  concrete  mixtures,  with  a  view  to  producing  a  given  result  in  the 
most  economic  manner,  involves  many  complications  which  have  heretofore  defied 
analysis. 

Many  different  methods  of  proportioning  have  been  suggested;  the  most  im- 
portant ones  may  be  characterized  as  follows : 

1.  Arbitrary  selection,  such  as  1:2:4  mix,  without  reference  to  the  size  or 

grading  of  the  fine  and  coarse  aggregate; 

2.  Density  of  aggregates  in  which  the  endeavor  is  made  to  secure  an  aggregate 

of  maximum  density; 

3.  Density  of  concrete  in  which  the  attempt  is  made  to  secure  concrete  of 

maximum  density; 

4.  Sieve  analysis,  in  which  the  grading  of  the  aggregates  is  made  to  approxi- 

mate some  predetermined  sieve  analysis  curve  which  is  considered  to  give 
the  best  results ; 

5.  Surface  area  of  aggregates. 

It  is  a  matter  of  common  experience  that  the  method  of  arbitrary  selection  in 
which  fixed  quantities  of  fine  and  coarse  aggregates  are  mixed  without  regard  to 
the  size  and  grading  of  the  individual  materials,  is  far  from  satisfactory.  Our  experi- 
ments have  shown  that  the  other  methods  mentioned  above  are  also  subject  to  serious 
limitations.  We  have  found  that  the  maximum  strength  of  concrete  does  not  depend 
on  either  an  aggregate  of  maximum  density  or  a  concrete  of  maximum  density, 
and  that  the  methods  which  have  been  suggested  for  proportioning  concrete  by 
sieve  analysis  of  aggregates  are  based  on  an  erroneous  theory.  All  of  the  methods 
of  proportioning  concrete  which  have  been  proposed  in  the  past  have  failed  to  give 
proper  attention  to  the  water  content  of  the  mix.  Our  experimental  work  has 
emphasized  the  importance  of  the  water  in  concrete  mixtures,  and  shown  that  the 
water  is,  in  fact,  the  most  important  ingredient,  since  very  small  variations  in  water 
content  produce  more  important  variations  in  the  strength  and  other  properties  of 
concrete  than  similar  changes  in  the  other  ingredients. 


•Reprinted  from   Minutes  of  the  Annual   Meeting  of  the   Portland   Cement  Association,   held 
in    New   York,    December,    1918. 


2  •*•  I  •  ;l  ;"  I^f it^trp&'ljRAi.  S»MATE^IALS  RESEARCH   LABORATORY 

New  Studies  of  Concrete  Mixtures 

During  the  past  three  years  a  large  number  of  investigations  have  been  under 
way  at  the  Structural  Materials  Research  Laboratory,  Lewis  Institute,  Chicago, 
which  throw  considerable  new  light  on  the  subject  of  proportioning  concrete.  These 
investigations  are  being  carried  out  through  the  cooperation  of  the  Institute  and 
the  Portland  Cement  Association.  These  studies  have  covered  an  investigation 
of  the  inter-relation  of  the  following  factors: 

1.  The  consistency  (quantity  of  mixing  water). 

2.  The  size  and  grading  of  aggregates. 

3.  The  mix  (proportion  of  cement). 

Any  comprehensive  study  of  proportioning  concrete  must  take  into  account  all  of 
these  factors. 

During  this  period  about  50,000  tests  have  been  carried  out  which  have  a 
bearing  on  this  subject.  These  tests  have  been  largely  confined  to  compression 
tests  of  concrete  and  mortars.  These  investigations  have  given  us  a  new  insight 
into  the  factors  which  underlie  the  correct  proportioning  of  concrete  mixtures  and 
show  the  limitations  of  older  methods.  Certain  phases  of  these  investigations  are 
still  under  way. 

The  following  may  be  mentioned  as  among  the  most  important  principles 
which  have  been  established  with  reference  to  the  design  of  concrete  mixtures. 
In  a  brief  report  of  this  kind  it  is  impracticable  to  present  more  than  an  putline  of 
the  methods  of  applying  the  principles  to  practical  problems.  In  only  a  few  instances 
are  experimental  data  given  on  which  these  conclusions  are  based. 

1.  With  given  concrete  materials  and  conditions  of  test  the  quantity  of  mixing 

water  used  determines  the  strength  of  the  concrete,  so  long  as  the  mix 
is  of  a  workable  plasticity. 

2.  The  sieve  analysis  furnishes  the  only  correct  basis  for  proportioning  ag- 

gregates in  concrete  mixtures. 

•  3.  A  simple  method  of  measuring  the  effective  size  and  grading  of  an  ag- 
gregate has  been  developed.  This  gives  rise  to  a  function  known  as  the 
"fineness  modulus"  of  the  aggregate. 

4.  The  fineness  modulus  of  the  aggregate  furnishes  a  rational  method   for 

combining  materials  of  different  size  for  concrete  mixtures. 

5.  The  sieve  analysis  curve  of  the  aggregate  may  be  widely  different  in  form 

without  exerting  any  influence  on  the  concrete  strength. 

6.  Aggregate  of  equivalent  concrete-making  qualities  may  be  produced  by  an 

infinite  number  of  different  gradings  of  a  given  material. 

7.  Aggregates  of  equivalent  concrete-making  qualities  may  be  produced  from 

materials  of  widely  different  size  and  grading. 

8.  In  general,  fine  and  coarse  aggregates  of  widely  different  size  or  grading 

can  be  combined  in  such  a  manner  as  to  produce  similar  results  in  con- 
crete. 

9.  The  aggregate  grading  which  produces  the  strongest  concrete  is  not  that 

giving  the  maximum  density  (lowest  voids).    A  grading  coarser  than  that 
giving  maximum  density  is  necessary  for  highest  concrete  strength. 

10.  The  richer  the  mix,  the  coarser  the  grading  should  be  for  an  aggregate  of 

given  maximum  size ;  hence,  the  greater  the  discrepancy  between  max- 
imum density  and  best  grading. 

11.  A  complete  analysis  has  been  made  of  the  water-requirements  of  concrete 

mixes.     The  quantity  of  water  required  is  governed  by  the   following 
factors : 

(a)  The  condition  of  "workability"  of  concrete  which  must  be  used 

— the  relative  plasticity  or  consistency; 

(b)  The  normal  consistency  of  the  cement; 

(c)  The  size  and  grading  of  the  aggregate — measured  by  the  fine- 

ness modulus; 


DESIGN  OF  CONCRETE  MIXTURES  3 

(d)  The  relative  volumes  of  cement  and  aggregate — the  mix; 

(e)  The  absorption  of  the  aggregate; 

(f)  The  contained  water  in  aggregate. 

12.  There  is  an  intimate  relation  between  the  grading  of  the  aggregate  and  the 

quantity  of  water  required  to  produce  a  workable  concrete. 

13.  The  water  content  of  a  concrete  mix  is  best  considered  in  terms  of  the 

volume  of  the  cement — the  water-ratio. 

14.  The  shape  of  the  particle  and  the  quality  of  the  aggregate  have  less  in- 

fluence  on   the   concrete   strength   than   has   been    reported   by  other   ex- 
perimenters. 

Effect  of  Quantity  of  Mixing  Water  on  the  Strength  of  Concrete 

Fig.  1  shows  the  relation  between  the  compressive  strength  and  the  water  con- 
tent for  28-day  tests  of  6  by  12-in.  concrete  cylinders.  Mixes  from  1 :15  to  neat 
cement  were  used;  each  mix  was  made  up  of  aggregates  ranging  in  size  from  14- 
mesh  sand  up  to  \l/2-\n.  gravel;  a  wide  range  in  consistencies  was  used  for  all 
mixes  and  gradings. 

The  water  content  of  the  concrete  is  expressed  as  a  ratio  to  the  volume  of 
cement,  considering  that  the  cement  weighs  94  Ib.  per  en.  ft.  Distinguishing  marks 
are  used  for  each  mix,  but  no  distinction  is  made  between  aggregates  of  different 
size  or  different  consistencies. 


400 


Wtrter-//o  to 


of  Ce/vexf  /r»,X 


FIG.    1.      RELATION   BETWEEN    STRENGTH    OF   CONCRETE   AND    WATER    CONTENT 

Twenty-eight-day  compression  tests  of  6  by  12-inch  cylinders.      (Series  83.) 

When  the  compressive  strength  is  platted  against  the  water  ratio  in  this  way, 
a  smooth  curve  is  obtained,  due  to  the  overlapping  of  the  points  for  different  mixes. 
Values  from  dry  concretes  have  been  omitted.  If  these  were  used  we  should  obtain 
a  series  of  curves  dropping  downward  and  to  the  left  from  the  curve  shown.  It  is 
seen  at  once  that  the  size  and  grading  of  the  aggregate  and  the  quantity  of  cement 
are  no  longer  of  any  importance  except  in  so  far  as  these  factors  influence  the 
quantity  of  water  required  to  produce  a  workable  mix.  This  gives  us  an  entirely 
new  conception  of  the  function  of  the  constituent  materials  entering  into  a  concrete 
mix  and  is  the  most  basic  principle  which  has  been  brought  out  in  our  studies  of 
concrete. 


'4r4-5-f.fi 


4  STRUCTURAL  MATERIALS   RESEARCH   LABORATORY 

The  equation  of  the  curve  is  of  the  form, 

A 
S=- (1) 

B* 

where  5  is  the  compressive  strength  of  concrete  and  x  is  the  ratio  of  the  volume 
of  water  to  the  volume  of  cement  in  the  batch.  A  and  B  are  constants  whose  values 
depend  on  the  quality  of  the  cement  used,  the  age  of  the  concrete,  curing  conditions, 
etc. 

This  equation  expresses  the  law  of  strength  of  concrete  so  far  as  the  pro- 
portions of  materials  are  concerned.  It  is  seen  that  for  given  concrete  materials 
the  strength  depends  on  only  one  factor — the  ratio  of  water  to  cement.  Equations 
which  have  been  proposed  in  the  past  for  this  purpose  contain  terms  which  take 
into  account  such  factors  as  quantity  of  cement,  proportions  of  fine  and  coarse 
aggregate,  voids  in  aggregate,  etc.,  but  they  have  uniformly  omitted  the  only  term 
which  is  of  any  importance;  that  is,  the  water. 

For  the  conditions  of  these  tests,  equation  (1)  becomes, 


(2) 


The  relation  given  above  holds  so  long  as  the  concrete  is  not  too  dry  for  max- 
imum strength  and  the  aggregate  not  too  coarse  for  a  given  quantity  of  cement; 
in  other  words,  so  long  as  we  have  a  workable  mix. 

Other  tests  made  in  this  laboratory  have  shown  that  the  character  of  the  ag- 
gregate makes  little  difference  so  long  as  it  is  clean  and  not  structurally  deficient. 
The  absorption  of  the  aggregate  must  be  taken  into  account  if  comparison  is  being 
made  of  different  aggregates. 

The  strength  of  the  concrete  responds  to  changes  in  water,  regardless  of  the 
reason  for  these  changes.  The  water-ratio  may  be  changed  due  to  any  of  the 
following  causes : 

1.  Change  in  mix  (cement  content). 

2.  Change  in  size  or  grading  of  aggregate. 

3.  Change  in  relative  consistency. 

4.  Any  combination  of  (1)  to  (3). 

In  certain  instances  a  1 :9  mix  is  as  strong  as  a  1 :2  mix,  depending  only  on 
water  content.  It  should  not  be  concluded  that  these  tests  indicate  that  lean  mixes 
can  be  substituted  for  richer  ones  without  limit.  We  are  always  limited  by  the 
necessity  of  using  sufficient  water  to  secure  a  workable  mix.  So  in  the  case  of 
the  grading  of  aggregates.  The  workability  of  the  mix  will  in  all  cases  dictate  the 
minimum  quantity  of  water  that  can  be  used.  The  importance  of  the  workability 
factor  in  concrete  is  therefore  brought  out  in  its  true  relation. 

The  problem  of  designing  concrete  mixes  resolves  itself  into  this : 
To  produce  a  workable  concrete  which  has  a  given  water-ratio  using  a  minimum 
quantity  of  cement ;  or  the  converse,  to  produce  a  workable  concrete  with  a  minimum 
water-ratio  using  a  given  quantity  of  cement.  The  methods  for  securing  the  best 
grading  of  aggregate  and  the  use  of  the  driest  concrete  which  is  workable  are  thus 
seen  to  be  only  devices  which  enable  us  to  accomplish  the  above-mentioned  results. 

Fineness  Modulus  of  Aggregate 

The  experimental  work  carried  out  in  the  laboratory  has  given  rise  to  what  we 
term  the  fineness  modulus  of  the  aggregate.    This  function  furnishes  a  method  of 
measuring  the  size  and  grading  of  the  aggregate.    It  may  be  defined  as  follows : 
The  sum  of  the  percentages  in  the  sieve  analysis  of  the  aggregate  divided  by  100. 

The  sieve  analysis  is  determined  by  using  the,  following  sieves  from  the  Tyler 
standard  series:  100,  48,  28,  14,  8,  4,  ^-in.,  %-in.  and  1^-in.  These  sieves  are 
made  of  square-mesh  wire  cloth.  Each  sieve  has  a  clear  opening  just  double  the 


DESIGN  OF  CONCRETE  MIXTURES  5 

Table  1 
METHOD  OF  CALCULATING  FINENESS  MODULUS  OF  AGGREGATES 

The  sieves  used  are  commonly  known  as  the  Tyler  standard  sieves.    Each  sieve 
has  a  clear  opening  just  double  that  of  the  preceding  one. 

The  sieve  analysis  may  be  expressed  in  terms  of  volume  or  weight. 

The  fineness  modulus  of  an  aggregate  is  the  sum  of  the  percentages  given  by 
the  sieve  analysis,  divided  by  100. 


Per  Cent 

Sieve  Analysis  of  Aggregates 
of  Sample  Coarser  than  a  Given  Sieve 

Sieve 
Size 

Size  of 
Square  Opening 
in.              mm. 

Sand 

Pebbles 

Concrete 
Aggregate 
(G)* 

Fine    Medium 
(A)          (B) 

Coarse 
(C) 

Fine 
(D) 

Medium 
(E) 

Coarse 
(F) 

100-mesh   

.0058 
.0116 
.0232 
.046 
.093 
.185- 
.37, 
.75 
1.5-, 

.147 
.295 
.59 
1.17 
2.36 
4.70 
9.4 
18.8 
38.1 

82 
52 
20 
0 
0 
0 
0 
0 
0 

91 
70 
46 
24 
10 
0 
0 
0 
0 

97 
81 
63 
44 
25 
0 
0 
0 
0 

100 
100 
100 
100 
100 
86 
51 
9 
0 

100 
100 
100 
100 
100 
95 
66 
25 
0 

100 
100 
100 
100 
100 
100 
86 
50 
0 

98 
92 
86 
81 
78 
71 
49 
19 
0 

48-mesh   
28-mesh   

14-mesh   
8-mesh 

4-mesh   

$/£-  in  

Ij^-in     

Fineness  Modulus 1.54 


2.41 


3.10 


6.46 


6.86 


7.36 


5.74 


'Concrete  aggregate  "G"  is  made  up  of  25%  of  sand  "B"  mixed  with  75%  of  pebbles  "E." 
Equivalent  gradings  would  be  secured  by  mixing  33%  sand  "B"  with  67%  coarse  pebbles  "F"; 
28%  "A"  with  72%  "F,"  etc.  The  proportion  coarser  than  a  given  sieve  is  made  up  by  the 
addition  of  these  percentages  of  the  corresponding  size  of  the  constituent  materials. 


/oo 


FIG.    2. 


METHOD    OF    PLOTTING    SIEVE    ANALYSIS    OF    AGGREGATES 
Sieve  analysis  curves  for  aggregates   B,   E  and   G  in  Table   1. 


6  STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 

width  of  the  preceding  one.  The  exact  dimensions  of  the  sieves  and  the  method 
of  determining  the  fineness  modulus  will  be  found  in  Table  1.  It  will  be  noted 
that  the  sieve  analysis  is  expressed  in  terms  of  the  percentages  of  material  by 
volume  or  weight  coarser  than  each  sieve. 

A  well-graded  torpedo  sand  up  to  No.  4  sieve  will  give  a  fineness  modulus  of 
about  3.00;  a  coarse  aggregate  graded  4-1^2  in.  will  give  fineness  modulus  of  about 
7.00;  a  mixture  of  the  above  materials  in  proper  proportions  for  a  1 :4  mix  will 
have  a  fineness  modulus  of  about  5.80.  A  fine  sand  such  as  drift-sand  may  have  a 
fineness  modulus  as  low  as  1.50. 

Sieve  Analysis  of  Aggregates 

There  is  an  intimate  relation  between  the  sieve  analysis  curve  for  the  aggregate 
and  the  fineness  modulus ;  in  fact,  the  fineness  modulus  enables  us  for  the  first  time 
to  properly  interpret  the  sieve  analysis  of  an  aggregate.  If  the  sieve  analysis  of  an 
aggregate  is  platted  in  the  manner  indicated  in  Fig.  2;  that  is,  using  the  per  cent 
coarser  than  a  given  sieve  as  ordinate,  and  the,,  sieve  size  (platted  to  logarithmic 
scale)  as  abscissa,  the  fineness  modulus  of  the  aggregate  is  measured  by  the  area 
below  the  sieve  analysis  curve.  The  dotted  rectangles  for  aggregate  "G"  show 
how  this  result  is  secured.  Each  elemental  rectangle  is  the  fineness  modulus  of  the 
material  of  that  particular  size.  The  fineness  modulus  of  the  graded  aggregate  is 
then  the  summation  of  these  elemental  areas.  Any  other  sieve  analysis  curve  which 
will  give  the  same  total  area  corresponds  to  the  same  fineness  modulus  and  will 
require  the  same  quantity  of  water  to  produce  a  mix  of  the  same  plasticity  and 
gives  concrete  of  the  same  strength,  so  long  as  it  is  not  too  coarse  for  the  quantity 
of  cement  used. 

The  fineness  modulus  may  be  considered  as  an  abstract  number ;  it  is  in  fact  a 
summation  of  volumes  of  material.  There  are  several  different  methods  of  com- 
puting it,  all  of  which  will  give  the  same  result.  The  method  given  in  Table  1 
is  probably  the  simplest  and  most  direct. 

Some  of  the  mathematical  relations  involved  are  of  interest.  The  following 
expression  shows  the  relation  between  the  fineness  modulus  and  the  size  of  the 
particle : 

m  =  7.94  +  3.32  log  d (3) 

Where  m  —  fineness  modulus 

d  =  diameter  of  particle  in  inches 

This  relation  is  perfectly  general  so  long  as  we  use  the  standard  set  of  sieves 
mentioned  above.  The  constants  are  fixed  by  the  particular  sizes  of  sieves  used 
and  the  units  of  measure.  Logarithms  are  to  the  base  10. 

This  relation  applies  to  a  single-size  material  or  to  a  given  particle.  The 
fineness  modulus  is  then  a  logarithmic  function  of  the  diameter  of  the  particle. 
This  formula  need  not  be  used  with  a  graded  material,  since  the  value  can  be 
secured  more  easily  and  directly  by  the  method  used  in  Table  1.  It  is  applicable 
to  graded  materials  provided  the  relative  quantities  of  each  size  are  considered, 
and  the  diameter  of  each  group  is  used.  By  applying  the  formula  to  a  graded 
material  we  would  be,  calculating  the  values  of  the  separate  elemental  rectangles 
shown  in  Fig.  2.  \ 

Fineness  Modulus  Strength  Relation  for  Concrete 

Many  different  series  of  tests  have  shown  that  for  a  given  plastic  condition  of 
concrete  and  the  same  mix  there  is  an  intimate  relation  between  the  fineness  modulus 
of  the  aggregate  and  the  strength  and  other  properties  of  the  concrete.  We  have 
seen  that  the  reason  for  this  result  is  found  in  the  fact  that  the  fineness  modulus 
simply  reflects  the  changes  in  water-ratio  necessary  to  produce  a  given  plastic 
condition. 

Figs.  3  and  4  give  the  results  of  certain  compression  tests  which  bring  out  the 
relation  between  the  strength  of  the  concrete  and  the  fineness  modulus  of  the 
aggregate.  It  will  be  noted  from  Fig.  3  that  a  separate  curve  may  be  drawn  for 
each  mix.  In  each  case  there  is  a  steady  increase  in  the  compressive  strength  of 


DESIGN  OF  CONCRETE  MIXTURES 


.      7 


S000 


I 


<s 


zoo 


FIG.    3. 


RELATION    BETWEEN   FINENESS    MODULUS    OF   AGGREGATE 
AND   STRENGTH    OF   CONCRETE 


Sand   and   pebble   aggregate   graded   0- 
cylinders.      (Series  78.) 


inch;    28-day   compression   tests   of   6    by    12-inch 


The  sieve  analyses  of  aggregates  are  given  below: 


Range             Fineness 
in  Size            Modulus 

Per  Cent  Coarser  than  Each  Si 

eve 

100 

48 

28 

14 

8 

4 

H 

*A 

iy*  2 

0-1 

14               4  30 

89 
95 
98 
99 
100 
100 
100 
100 

82 
89 
94 
98 
99 
99 
100 
100 

72 
82 
88 
95 
97 
98 
99 
99 

62 
73 
80 
90 
92 
95 
96 
98 

51 
61 
69 
81 
85 
88 
91 
94 

38 

47 
55 
68 
72 
77 
80 
86 

25 
32 
38 
49' 
53 
58 
62 
68 

11 

14 
18 
24 
27 
30 
32 
37 

0 

0 
0 
0 
0 
0 
0 
0 

4.93 

5.40 

6  04 

6  25 

6  45 

6.60 

.  6.82 

STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 


v^ 


/.OO 


FIG.   4.     RELATION   BET/VEEN   FINENESS   MODULUS   OF  AGGREGATE 
AND   STRENGTH  OF  CONCRETE 

Twenty-eight-day  compression  tests  of  6  by  12-inch  cylinders.  (Series  78.)  Sand  and  pebble 
aggregate  graded  to  sizes  shown.  The  contrast  between  the  relation  shown  by  these  tests  and 
those  in  Fig.  3  should  be  noted. 

The  sieve  analyses  of  aggregates  are  given  below: 


Range 
in  Size 

Fineness 
Modulus 

Per    Cent    Coarser 

than    Each    Sieve 

100 

48 

28 

14 

8 

4 

y& 

y\ 

1/2 

2 

0-14 

2  16 

95 
96 
96 
98 
99 
100 

84 
90 
91 
96 
98 
99 

37 
62 
83 
91 
95 
97 

0 
40 
71 
83 
90 
94 

0-4      .  .  

3.06 

18 
54 
71 
81 
87 

0 
31 
54 
68 

77 

0 
31 
49 
62 

0 
24 
42 

0 

14 

0 

0-     ^  

4.26 

o-    &  

5.24 

0-  1%  

6.04 

0-  2     , 

.      6.72 

DESIGN  OF  CONCRETE  MIXTURES 
Table  2 

EFFECT  OF  GRADING  OF  AGGREGATES  ON  THE  STRENGTH 

OF  CONCRETE 


Compression  tests  of  6  by  12-in.  concrete  cylinders. 

Mix  1 :5  by  volume ;  age  at  test,  28  days ;  stored  in  damjl  sand ;  tested  damp. 

Aggregates — sand  and  pebbles  from  Elgin,  111.  Aggregates  were  screened  to 
different  sizes  and  recombined  to  conform  to  predetermined  sieve  analyses. 

The  aggregates  were  made  up  in  such  a  manner  as  to  give  the  widest  variations 
in  the  grading  of  the  particles.  All  gradings  had  one  common  property,  in  that  the 
fineness  modulus  was  exactly  the  same — m  =  6.04.  The  fineness  modulus  of  the 
aggregate  is  the  sum  of  the  percentages  in  the  sieve  analysis,  divided  by  100. 

The  same  quantity  of  water  was  used  in  all  specimens  of  a  given  consistency. 
The  110%  consistency  contains  10%  more  water  than  the  100%. 

Each  specimen  was  made  from  a  separate  batch. 

Each  value  in  the  strength  tests  is  the  average  >from  5  tests  made  on  different 
days.  (From  Series  78.) 


Ref. 

Fineness 
Sieve  Analysis  of  Aggregate                  Modulus 
Per  Cent  Coarser  than  Each  Sieve           of  Aggre- 

Surface  Area 
of  Aggregate  sq.  in. 

Compressive  Strength 
of  Concrete  at  28  days 
(lb.  per  sq.  in.) 

per  lb.  of 

per  g.  ot 
Cement 

100%  Con- 
sistency 

110%  Con- 
sistency 

No.   100 

48     28 

14 

8       4 

tt 

H 

1  %  1  1A  2      gate      Aggregate 

40     99 

98     95 

90 

81     68 

49 

24 

0 

6.04 

602 

8.8 

3,300 

2,890 

259     99 

98     96 

92 

84     67 

46 

22 

0 

6.04 

569 

8.2 

2,950 

2,650 

260     98 

97     93 

88 

80     67 

52 

29 

0 

6.04 

764 

11.4 

3,120 

2,760 

261     97 

94     91 

85 

77     67 

58 

35 

0 

6.04 

999 

15.2 

3,140 

2,790 

262     95 

92     87 

82 

75     67 

67 

39 

0 

6.04 

1,292 

20.1 

3,100 

2,800 

263     95 

90     84 

78 

73     67 

62 

55 

0 

6.04 

1,451 

23.0 

2,830 

2,740 

264     95 

89     82 

75 

67     67 

67 

62 

0 

6.04 

1,565 

25.2 

2,680 

2,580 

265   100 

97     91 

79 

72     67 

58 

40 

0 

6.04 

761 

11.9 

3,070 

2,690 

266  100 

97     93 

88 

83     67 

50 

27 

7     0 

6.04 

616 

9.0 

3,080 

2,790 

267     99 

97,    94 

86 

77     67 

47 

27 

16          0 

6.04 

709 

10.5 

3,150 

2,710 

268     98 

95     90 

83 

83     83 

50 

22 

0 

6.04 

834 

12.6 

3,080 

2,500 

269     98 

94     90 

86 

83     80 

55 

18 

0 

6.04 

898 

13.3 

3,050 

2,550 

270     96 

90     80 

80 

80     80 

60 

39 

0 

6.04 

1,391 

21.5 

2,970 

2,550 

271   100 

96     92 

87 

81     75 

50 

23 

0 

6.04 

672 

10.0 

2,930 

2,710 

272     95 

91     87 

82 

77     73 

59 

40 

0 

6.04 

1,315 

20.2 

3,000 

2,580 

273     99 

95     88 

80 

76     73 

61 

32 

0 

6.04 

911 

13.9 

2,950 

2,740 

274     90 

85     81 

78 

75     73 

66 

56 

0 

6.04 

1,992 

31.3 

x  2,680 

2,440 

275  100 

93     82 

73 

73     73 

63 

47 

0 

6.04 

1,076 

16.7 

2,820 

2,620 

276  100 

100  100 

92 

81     60 

45 

26 

0 

6.04 

390 

5.6 

3,040 

2,780 

277  100 

98     95 

90 

80     60 

50 

31 

0 

6.04 

557 

8.3 

2,900 

2,770 

278  100 

99     96 

92 

84     55 

50 

28 

0 

6.04 

483 

7.0 

2,940 

2,750 

279  100 

99     96 

91 

80     5*0 

50 

38 

0 

6.04 

514 

7.6 

3,080 

2,750 

280     98 

84     84 

84 

84     57 

57 

57 

0 

6.04 

1,276 

19.7 

3,000 

2,780 

281     99 

98     91 

86 

80     76 

38 

38 

0 

6.04 

701 

10.4 

2,940 

2,700 

282     99 

98     91 

86 

80     76 

46 

30 

0 

6.04 

697 

10.2 

3,020 

2,660 

283     99 

98     91 

86 

80     76 

61 

15 

0 

6.04 

689 

10.1 

2,930 

2,670 

284     99 

98     91 

85 

80     76 

67 

8 

0 

6.04 

685 

9.9 

2,970 

2,630 

Av 

6.04 

904 

13.8 

2,990 

2,690 

^Minimum  Value                  '                     •               .... 

390 

5.6 

2,680 

2,440 

1,992 

31.3 

3,300 

2,890 

Mean  Variation 

from 

Average 

—  per  ce 

nt 

34.4 

37.2 

3.41 

3.04 

10  STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 

the  concrete  as  the  fineness  modulus  of  the  aggregate  increases,  until  a  certain  value 
is  reached  which  corresponds  to  a  maximum  point.  It  will  be  noted  also  that  this 
maximum  point  corresponds  to  higher  and  higher  values  of  fineness  modulus  as  the 
quantity  of  cement  in  the  mix  is  increased.  In  other  words,  the  maximum  strength 
comes  at  a  fineness  modulus  of  about  5.80  for  the  1  :9  mix  and  about  6.40  for  the 
1  :4  mix.  In  these  tests  the  different  values  of  the  fineness  modulus  were  secured 
by  using  a  preponderance  of  the  coarser  sizes,  but  in  all  cases  maintaining  the  same 
limiting  size,  that  is,  1^4  in- 

In  Fig.  4  is  foui^I  a  similar  relation  between  the  strength  and  the  fineness 
modulus,  except  that  no  maximum  point  is  found.  This  condition  arises  from  the 
fact  that  the  maximum  size  of  the  aggregate  is  increasing  without  changing  the 
type  of  the  sieve  analysis  curve,  consequently  the  fineness  modulus  strength  curve 
continues  to  rise  indefinitely.  The  height  to  which  the  curve  rises  is  limited  only 
by  the  maximum  size  of  aggregate  which  may  be  used.  It  is  important  to  note 
that  there  is  no  conflict  between  the  indications  of  Figs.  3  and  4. 

For  all  practical  purposes  and  for  ordinary  ranges  in  concrete  mixes  the  fine- 
ness modulus  strength  relation  may  be  assumed  as  a  linear  one.  The  comparison 
of  the  true  and  approximate  relation  is  brought  out  in  the  discussion  of  the  "Water 
Formula"  below. 

A  given  value  for  the  fineness  modulus  of  an  aggregate  can  be  secured  with 
any  combination  of  percentages  in  the  sieve  analysis  which  gives  the  same  total, 
consequently,  an  infinite  variety  of  gradings  may  be  found  which  give  aggregate 
of  the  same  concrete  strength.  Table  2  gives  the  results  of  groups  of  tests  which 
bring  out  the  wide  variation  which  may  be  made  in  the  grading  of  aggregate  with- 
out producing  any  essential  variation  in  the  concrete  strength.  Twenty-seven  differ- 
ent gradings  of  the  same  aggregate  were  made  up.  These  gradings  covered  the 
widest  possible  range,  but  they  had  one  property  in  common;  that  is,  a  fineness 
modulus  of  6.04.  All  specimens  were  mixed  with  the  same  quantity  of  cement  and 
water.  Separate  sets  of  specimens  were  made  of  two  different  consistencies.  The 
mean  variation  from  the  average  strength  is  about  3%. 

Table  2  also  furnishes  some  interesting  data  on  the  surface-area  method  of 
proportioning  aggregates.  It  is  seen  that  there  is  the  widest  variation  in  the  surface 
area  of  the  aggregate  without  any  appreciable  difference  in  the  concrete  strength. 
Our  studies  have  clearly  shown  that  surface  area  is  not  a  satisfactory  basis  for  pro- 
portioning aggregates. 

Design  of  Concrete  Mixes 

In  accordance  with  our  previous  statements  the  problem  of  designing  concrete 
mixes  using  given  materials  resolves  itself  into  that  of  finding  the  combination 
which  with  a  given  water-ratio  will  give  a  concrete  of  suitable  workability  using  a 
minimum  of  cement. 

The  following  outline  will  make  clear  the  steps  to  be  followed  in  the  design 
of  concrete  mixes  on  the  basis  of  our  studies  of  concrete: 


STEPS  IN  THE  DESIGN  OF  CONCRETE  MIXTURES 

1.  Knowing  the  compressive  strength  required  of  the.  concrete,  determine  by 
reference  to  Fig.  1  the  maximum  water-ratio  which  may  be  used.  Sub- 
sequent steps  in  the  design  of  concrete  mixes  are  only  devices  for 
securing  a  workable  concrete  using  this  water-ratio  and  a  minimum  quan- 
tity of  cement.  It  is  obvious  that  a  given  water-ratio  can  be  secured  with 
a  minimum  of  cement  if  the  aggregate  is  graded  as  coarse  as  permissible 
(considering  its  size  and  the  mix  used)  and  if  we  use  the  driest  mix 
which  can  be  properly  placed.  Securing  a  coarse,  well-graded  aggregate, 
using  rich  mixes,  employing  the  driest  practicable  consistency,  using 
mechanical  methods  of  placing  concrete,  etc.,  are  all  methods  of  producing 
a  workable  mix  with  a  minimum  water-ratio.  Experience  or  trial  is  the 
only  guide  in  determining  the  relative  consistency  of  concrete  necessary 
in  the  work.  Obviously  the  driest  workable  consistency  should  be  used. 


DESIGN  OF  CONCRETE  MIXTURES  ]  1 

The  size  of  aggregate  available,  or  which  must  be  used,  and  the  other 
factors  will  furnish  a  guide  as  to  the  mix.  The  mix  is  expressed  as  one 
volume  of  cement  to  a  given  number  of  volumes  of  aggregate;  that  is, 
the  combined  fine  and  coarse  aggregate.  In  general,  some  allowance 
must  be  made  for  the  high  strengths  in  laboratory  tests.  In  other  words, 
a  water-ratio  somewhat  lower  than  that  given  for  the  required  strength 
in  Fig.  1  should  be  used.  For  convenience  in  the  subsequent  steps  we 
shall  deal  with  concrete  strength  instead  of  water-ratio  (as  in  Fig.  6), 
although  it  should  be  understood  that  it  is  the  water-ratio  which  fixes  the 
strength  so  long  as  we  have  a  plastic  mix. 

2.  Make  sieve  analysis  of  fine  and  coarse  aggregates,  using  Tyler  standard 

sieves  of  the  following  sizes:  100,  48,  28,  14,  8,  4,  J&,  %  and  \l/2  in. 
Express  sieve  analysis  in  terms  of  percentages  of  material  by  weight  (or 
separate  volumes)  coarser  than  each  of  the  standard  sieves. 

3.  Compute  fineness   modulus   of   each   aggregate  by  adding  the  percentages 

found  in  (2),  and  dividing  by  100. 

4.  Determine  the   "maximum   size"   of   aggregate   by   applying  the    following 

rules:  If  more  than  20%  of  aggregate  is  coarser  than  any  sieve  the 
maximum  size  shall  be  taken  as  the  next  larger  sieve  in  the  standard 
set;  if  between  11  and  20%  is  coarser  than  any  sieve,  maximum  size  shall 
be  the  next  larger  "half-sieve" ;  if  less  than  10%  is  coarser  than  certain 
sieves,  the  smallest  of  these  sieve  sizes  shall  be  considered  the  maximum 
size. 

5.  From  Table  3  determine  the  maximum  value  of  fineness  modulus  which 

may  be  used  for  the  mix,  kind  and  size  of  aggregate,  and  the  work  under 
consideration.  (The  values  in  Table  3  are  platted  in  Fig.  5.) 

6.  Compute  the  percentages  of  fine  and  coarse  aggregates  required  to  produce 

the  fineness  modulus  desired  for  the  final  aggregate  mixture  by  applying 
the  formula : 

A  — B 

p-=100  —      - (3) 

*  A  —  C 

where  p  =  percentage  of  fine  aggregate  in  total  mixture. 
A  =  fineness  modulus  of  coarse  aggregate. 
B  •=  fineness  modulus  of  final  aggregate  mixture. 
C  •=  fineness  modulus  of  fine  aggregate. 

Fig.  7  may  be  used  for  solving  Equation  3,  and  for  making  comparisons  of 
the  effect  of  certain  changes  in  proportions  of  fine  and  coarse  aggregates.    The\ 
distinction  between  fine  and  coarse  aggregate  is  solely  for  convenience  in  secur- 
ing a  uniform  grading;  the  envision  may  be  made  at  any  desired  point. 

7.  With  the  estimated  mix,  fineness  modulus  and  consistency  enter  Fig.  6  and 

determine  the  strength  of  concrete  produced  by  the  combination.  If  the 
strength  shown  by  the  diagram  is  not  that  required,  the  necessary  read- 
justment may  be  made  by  changing  the  mix,  consistency  or  size  and 
grading  of  the  aggregates. 

The  quantity  of  water  required  can  be  determined  from  Formula  4  below, 
or  approximately  from  Table  5. 

IMPORTANT  NOTE:  It  must  be  understood  that  the  values  in  Fig.  6 
were  determined  from  compression  tests  of  6  by  12-in.  cylinders  stored  for  28 
days  in  a  damp  place.  The  values  obtained  on  the  work  will  depend  on  such 
factors  as  the  consistency  of  the  concrete,  quality  of  the  cement,  methods  of 
mixing,  handling,  placing  the  concrete,  etc.,  and  on  age  and  curing  conditions. 

Strength  values  higher  than  given  for  relative  consistency  of  1.10  should 
seldom  be  considered  in  designing,  since  it  is  only  in  exceptional  cases  that  a 
consistency  drier  than  this  can  be  satisfactorily  placed.  For  wetter  concrete 
much  lower  strengths  must  be  considered. 


12  STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 

Table  3 

MAXIMUM  PERMISSIBLE  VALUES  OF  FINENESS  MODULUS 
OF  AGGREGATES 

For  mixes  other  than  those  given  in  the  table,  use  the  values  for  the  next 
leaner  mix. 

For  maximum  sizes  of  aggregate  other  than  those  given  in  the  table,  use  the 
values  for  the  next  smaller  size. 

Fine  aggregate  includes  all  material  finer  than  No.  4  sieve;  coarse  aggregate 
includes  all  material  coarser  than  the  No.  4  sieve.  Mortar  is  a  mixture  of  cement, 
water  and  fine  aggregate. 

This  table  is  based  on  the  requirements  for  sand-and-pebble  or  gravel  aggregate 
composed  of  approximately  spherical  particles,  in  ordinary  uses  of  concrete  in  rein- 
forced concrete  structures.  For  other  materials  and  in  other  classes  of  work  the 
maximum  permissible  values  of  fineness  modulus  for  an  aggregate  of  a  given  size 
is  subject  to  the  following  corrections: 

(1)  If  crushed  stone  or  slag  is  used  as  coarse  aggregate,  reduce  values  in 
table   by  0.25.     For   crushed   material   consisting   of   unusually   flat   or   elongated 
particles,  reduce  values  by  0.40. 

(2)  For  pebbles  consisting  of  flat  particles,  reduce  values  by  0.25. 

(3)  If  stone  screenings  are  used  as  fine  aggregate,  reduce  values  by  0.25. 

(4)  For  the  top  course  in  concrete  roads,  reduce  the  values  by  0.25.    If  finish- 
ing is  done  by  mechanical  means,  this  reduction  need  not  be  made. 

(5)  In  work  of  massive  proportions,  such  that  the  smallest  dimension  is  larger 
than  10  times  the  maximum  size  of  the  coarse  aggregate,  additions  may  be  made 
to  the  values  in  the  table  as  follows:  for  24-in.  aggregate  0.10;  for  1^-in.  0.20;  for 
3-in.  0.30;  for  6-in.  0.40. 

Sand  with  fineness  modulus  lower  than  1.50  is  undesirable  as  a  fine  aggregate* 
in  ordinary  concrete  mixes.  Natural  sands  of  such  fineness  are  seldom  found. 

Sand  or  screenings  used  for  fine  aggregate  in  concrete  must  not  have  a  higher 
fineness  modulus  than  that  permitted  for  mortars  of  the  same  mix.  Mortar  mixes 
are  covered  by  the  table  and  by  (3)  above. 

Crushed  stone  mixed  with  both  finer  sand*and  coarser  pebbles  requires  no 
reduction  in  fineness  modulus  provided  the  quantity  of  crushed  stone  is  less  than 
30%  of  the  total  volume  of  the  aggregate. 


Mix 

Size  of  Aggregate 

Cem.-Agg.         0-28 

0-14 

0-8       0-4      0-3*     0-H    0-*A*    0-tt  0-lin.*0-1^0-2.1*0-3m.0-4^*0-6in. 

1-12 

.20 
.30 
.40 
1.50 
L.60 
1.70 
1.85 
2.00 
2.25 

1.80 
1.85 
1.95 
2.05 
2.15 
2.30 
2.50 
2.70 
3.00 

2.40  2.95  3.35  3.80  4.20  4.60  5.00  5.35  5.75  6.20  6.60  7.00 
2.45  3.05  3.45  3.85  4.25  4.65  5.00  5.40  5.80  6.25  6.65  7.05 
2.55  3.20  3.55  3.95  4.35  4.75  5.15  5.55  5.95  6.40  6.80  7.20 
2.65  3.30  3.65  4.05  4.45  4.85  5.25  5.65  6.05  6.50  6.90  7.30 
2.75  3.45  3.80  4.20  4.6J)  5.00  5.40  5.80  6.20  6.60  7.00  7.45 
2.90  3.60  4.00  4.40  t.80  5.20  5.60  6.00  6.40  6.85  7.25  7.65 
3.10  3.90  4.30  4.70  5.10  5.50  5.90  6.30  6.70  7.15  7.55  8.00 
3.40  4.20  4.60  5.05  5.45  5.90  6.30  6.70  7.10  7.55  7.95  8.40 
3.80  4.75  5.25  5.60  6.05  6.50  6.90  7.35  7.75  8.20  8.65  9.10 

.9 

-6 

.5 

.4 

-3  

-2  : 

-i  

'Considered  as  "half-size"  sieves;  not  used  in  computing  fineness  modulus. 


DESIGN  OF  CONCRETE  MIXTURES  13 

Calculation  of  Water  Required  for  Concrete 

Because  of  the  important  influence  of  the  quantity  of  water  in  the  concrete  it 
is  desirable  to  have  a  sound  basis  for  proportioning  the  water.  The  quantity  of 
water  necessary  for  given  proportions  and  conditions  may  be  determined  by  the 
following  formula: 


=  R     —  p  +  (- ha  — c  j    n       

L  2          V  1.26m  / 


(4) 

where  x  =  water  required — ratio  to  volume  of  cement  in  batch  (water- 
ratio). 

R  —  Relative  consistency  of  concrete,  or  "workability  factor". 
Normal  consistency  (relative  consistency  =  1.00)  requires 
the  use  of  such  a  quantity  of  mixing  water  as  will  cause  a 
slump  of  ^2  to  1  in.  in  a  freshly  molded  6  by  12-in.  cylinder 
of  about  1 :4  mix  upon  withdrawing  the  form  by  a  steady, 
upward  pull.  A  relative  consistency  of  1.10  requires  the  use 
of  10%  more  water  and  under  the  above  conditions  will  give 
a  slump  of  about  5  to  6  in. 

p  z=  Normal  consistency  of  cement,  ratio  by  weight. 

m  =  Fineness  modulus  of  aggregate  (an  exponent). 

n  =  Volumes  of  mixed  aggregate  to  one  of  cement. 

a  •=  Absorption  of  aggregate,  ratio  of  water  absorbed  to  volume  of 
aggregate.  (Determined  after  immersion  in  water  for  3 
hours.  Average  values  for  crushed  limestone  and  pebbles 
may  be  assumed  as  0.02;  porous  sandstones  may  reach  0.08; 
very  light  and  porous  aggregate  may  reach  0.25.) 

c  —  Moisture  contained  in  aggregate,  ratio  of  water  contained  to 
volume  of  aggregate.  (Assume  as  zero  for  room-dry  ag- 
gregate.) 

This  formula  takes  account  of  all  the  factors  which  affect  the  quantity  of  water 
required  in  a  concrete  mixture.  These  factors  may  be  classified  as  follows : 

1.  "Workability"  factor,  or  the  relative  consistency  of  the  concrete.     This  is 

dictated  by  the  kind  of  work  being  done ;  concrete  must  be  more  plastic 
(which  generally  means  a  wetter  consistency)  in  reinforced  concrete 
building  construction  than  is  necessary  in  mass  work.  The  term  (R)  in 
the  equation  takes  care  of  this  factor.  (R)  may  vary  from,  say,  0.90  for 
a  dry  concrete  to  2.00  or  higher  for  very  wet  mixes. 

2.  Cement  factor,  which  is  made  up  of  two  parts :  the  quality  of  cement  so  far 

as  normal  consistency  is  concerned  (p)  ;  the  quantity  of  cement  in  the 
mix  (n). 

3.  The  aggregate  factor.    This  includes  the  three  terms  within  the  parenthesis 

in  Equation  4.  The  first  term,  involving  (m),  takes  account  of  the  size 
and  grading;  the  second  (a)  the  absorption,  and  the  third  (c)  the  water 
contained  in  the  aggregate. 

In  case  admixtures  of  any  kind  are  used,  another  term  must  be  inserted  in  the 
equation.  This  relation  has  been  fully  worked  out,  but  is  not  included  in  this 
report. 

Simplified  Water  Formula 

While  Equation  (4)  represents  the  true  water  relation,  it  is  somewhat  com- 
plicated by  the  fact  that  the  fineness  modulus  (m)  appears  as  an  exponent.  The 
equation  can  be  expressed  in  a  simpler  form  as  follows : 


f3  m  1 

=  R     -p+(0.22 +  a-c)n      


(5) 


This  equation  gives  values  for  ordinary  ranges  of  mix  and  grading  of  aggregate 
which  are  sensibly  the  same  as  given  by  Equation  (4). 


14 


STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 


* 


FIG.  5.    MAXIMUM  PERMISSIBLE  VALUES^OF  FINENESS  MODULUS  OF  AGGREGATE 

Graphical  reproduction  of  Table  3.  These  curves  are  based  o»'  the  requirements  of  sand 
and  pebble  aggregate.  For  crushed  stone  aggregate  the  values  must  be\reduced  as  noted  in 
the  table.  ^«^_ 


Maximum  Permissible  Values  of  Fineness  Modulus  of  Aggregates 

Since  a  maximum  practicable  value  of  fineness  modulus  is  found  for  each  size 
of  aggregate  and  mix,  it  is  necessary  to  place  certain  limits  on  the  value  which 
may  be  used  for  proportioning  materials  for  concrete  mixes.  Table  3  gives  limits 
which  will  be  found  practicable.  Subsequent  experience  may  dictate  certain  modi- 
fications in  the  details. 

The  purpose  of  Table  3  is  to  avoid  the  attempt  to  secure  an  aggregate  grading 
which  is  too  coarse  for  its  maximum  size  and  for  the  amount  of  cement  used.  It 
is  also  useful  in  prohibiting  attempts  to  use  sands  which  are  too  coarse  for  best 
results  in  concrete  mixtures.  For  instance,  it  would  be  found  from  this  table  that 
the  use  of  a  sand  of  the  nature  of  standard  Ottawa  sand  is  not  permitted  except 
in  mixes  1 :2  or  richer. 

The  curves  in  Figure  5  are  platted  directly  from  the  values  given  for  the  stand- 
ard sieves  in  Table  3. 

Chart  for  Design  of  Concrete  Mixes 

Fig.  6  is  a  nomographic  chart  for  the  design  of  concrete  mixes.  This  chart 
takes  account  of  the  following  four  factors: 

1.  The  mix  (cement  content).  X 

2.  The  relative  consistency.  * 

3.  The  grading  of  aggregate  (fineness  modulus)*' 

4.  The  compressive  strength  of  concrete.  ^ 


DESIGN  OF  CONCRETE  MIXTURES  16 

Given  any  three  of  these  factors  the  chart  enables  us  to  solve  for  the  fourth. 
This  chart  is,  of  course,  based  on  the  results  of  certain  tests.  For  practical  applica- 
tion these  values  must  generally  be  reduced  by  certain  factors,  which  will  depend 
on  the  judgment  of  the  designer.  In  order  to  furnish  some  basis  for  comparison, 
compression  tests  of  1 :3  standard  sand  mortars  from  the  cement  used  in  these  tests 
are  given. 

Suppose  we  consider  the  case  of  concrete  for  road  construction.  This  is  gen- 
erally specified  as  a  1:1J^:3  or  a  1:2:3  mix,  with  aggregate  graded  up  to  \l/2 
in.  These  mixes  are  about  the  same  as  what  have  been  termed  a  1 :4  mix,  the  exact 
equivalent  depending  on  the  particular  size  and  grading  of  the  fine  and  coarse  ag- 
gregate. Assume  that  gravel  aggregate  will  be  used,  graded  to  \l/2  in.  Table  3 
shows  that  we  may  use  a  fineness  modulus  as  high  as  6.00  —  .25  —  5.75.  Knowing 
the  sieve  analysis  and  fineness  modulus  of  both  sizes  of  aggregate,  apply  the  formula 
or  Fig.  7  to  determine  the  proportions  of  each  aggregate  which  must  be  mixed  to 
secure  this  value.  Assume  that  the  concrete  will  be  mixed  to  a  relative  consistency 
of  1.10,  which  is  of  such  plasticity  as  will  g'ive  a  slump  of  5  to  6  in.  in  the  test  de- 
scribed above.  Place  a  straightedge  in  Fig.  6  on  mix  1 :4  and  fineness  modulus 
5.75,  and  mark  the  point  where  it  crosses  the  reference  line  for  consistency;  from 
this  point  project  the  line  horizontally  (as  indicated  in  other  examples)  to  relative 
consistency  1.10.  It  will  be  seen  that  'this  gives  a  compressive  strength  of  3,400  Ib. 
per  sq.  in.  at  28  days. 

r 
Table  4 

EXAMPLE  OF  INFLUENCE  OF  QUANTITY  OF  MIXING  WATER 
ON  THE  STRENGTH  OF  CONCRETE 

Values  calculated  from  equation 

A         14,000 

S  = = 

B*         8.2* 

Where  S  =  Compressive  strength  of  concrete   (Ib.  p^er  sq.  in.). 

x  =  Water-ratio  (an  exponent). 

A  and  B  are  constants  whose  values  depend  on  quantity  of  cement  and 
other  conditions  of  the  test.  The  values  given  for  A  and  B  are  based  on 
28-day  tests  of  1 :4  mix,  pebble  aggregate  graded  0-lj4-in.,  fineness  modulus 
5.75. 

The  water-ratio  is  equivalent  to  the  cubic  feet  of  water  to  1  sack  (1  cu.  ft.) 
of  cement. 

The  strength  values  are  solely  for  comparative  purposes  in  showing  the  influ- 
ence of  changing  the  water  content. 

Compressive  Strength  of  Concrete  at  28  Days 
Water  in  a  1-Bag  Batch        Relative  Consistency          Lb.  per  Sq.  In.  Relative  Strength 


Gallons 

Water-Ratio  (x) 

Per  Cent 

(S) 

Per  Cent 

5.75 

.77 

100 

2,770 

100 

6.0 

.80 

104 

2,600 

94 

6.25 

.84 

109 

2,400 

87 

6.5 

.87 

113 

2,250 

81 

7.0 

.94 

122 

1,950 

70 

7.5 

1.01 

131 

1,670 

60 

8.0 

1.07 

139 

1,470 

53 

9.0 

1.21 

157 

1,100 

40 

10.0 

1.34 

174 

830 

30 

12.0 

1.60 

208 

480 

17 

15.0 

2.00 

260 

200 

7 

16  STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 

Table  5 
QUANTITY  OF  MIXING  WATER  REQUIRED  FOR  CONCRETE 


[3  /  .30  \     1 

—  n-{_     [  --  La  —  c)n 
2  Vl.26m  )     \ 


Where  x  =  Water  required  —  ratio  to  volume  of  cement  in  batch   (water- 

ratio). 
R  —  Relative  consistency,  or  "workability  factor."    Where  R  =  1.00 

the  concrete  is  said  to  be  of  "normal  consistency." 
p  —  Normal  consistency  of  cement  by  weight  (assume  p  =  0.23). 
m  =  Fineness  modulus  of  aggregate. 

n  =  Volume  of  mixed  aggregate  to  one  volume  of  cement. 
a  =  Absorption  of  aggregate,  ratio  of  water  absorbed  to  volume  of 

aggregate. 
c  =  Moisture  in  aggregate,  ratio  of  water  contained  to  volume  of 

aggregate. 

(a  —  c)  =  Net  absorption  of  aggregate  by  volume. 

In  this  table  (a  —  c)  is  assumed  as  0.02.  In  other  words  the  net  quantity  of  water 
taken  by  the  aggregate  is  2%  by  volume.  This  value  may  be  used  for  ordinary 
limestones  and  pebbles.  For  crushed  trap  and  granite  it  is  somewhat  high.  It  is 
too  high  in  any  case  where  the  aggregate  is  saturated  with  water. 

A  relative  consistency  of  1.00  (normal  consistency)  requires  the  use  of  such  a 
quantity  of  mixing  water  as  will  cause  a  slump  of  %  to  1  in.  in  a  freshly  molded 
6  by  12-in.  cylinder  of  about  1  :4  mix  upon  withdrawing  the  form  by  a  steady,  upward 
pull.  This  consistency  is  somewhat  dry  for  most  concrete  work,  but  can  be  used 
where  light  tamping  is  practicable. 

A  relative  consistency  of  1.10  (10%  more  water  than  required  for  normal 
consistency)  represents  about  the  driest  concrete  which  can  be  satisfactorily  used 
in  concrete  road  construction.  Under  the  conditions  mentioned  above,  this  con- 
sistency will  give  a  slump  of  about  5  to  6  in. 

A  relative  consistency  of  1.25  represents  about  the  wettest  consistency  which 
should  be  used  in  reinforced  concrete  building  construction.  Under  the  conditions 
mentioned  above,  this  consistency  will  give  a  slump  of  about  8  to  9  in. 

For  mixes  and  fineness  moduli,  other  than  those  given  in  the  table,  approxi- 
mate values  may  be  determined  by  interpolation.  For  specific  cases  use  the  formula. 


Mix 
Cem.-Agg. 
by  Volume 

Gallons  of  Water  per  Sack  of  Cement 
Using  Aggregates  of  Different  Fineness  Moduli 

1.50 

2.00 

2.50 

3.00 

3.50 

4.00 

4.50       5.00 

5.50 

6.00 

6.50 

7.00 

Relative  Consistency  —  (R)  =  1 

.00 

1-12.  . 

23.5 
18.1 
14.7 
13.0 
11.2. 
9.5 
7.8 
6.0 
4.3 

21.4 
16.7 
13.5 
12.0 
10.4 
8.9 
7.2 
5.7 
4.1 

19.5 
15.2 
12.3 
11.0 
9.5 
8.2 
6.7 
5.4 
3.9 

17.8 
14.0 
11.4 
10.2 
8.9 
7.7 
6.3 
5.1 
3.8 

16.4 
12.9 
10.6 
9.5 
8.3 
7.2 
6.0 
4.9 
3.7 

15.2 
12.0 
9.9 
8.9 
7.8 
6.8 
5.7 
4.7 
3.6 

139       12.9 
11.0       10.2 
9.1          8.6 
8.3         7.7 
7..4        6.9 
6.3         6.0 
5.4         5.1 
4.5         4.3 
3.5         3.4 

12.0 
9.6 
8.0 
7.3 
6.4 
5.7 
4.9 
4.1 
3.3 

11.1 
9.0 
7.6 
6.8 
6.1 
5.4 
4.6 
4.0 
3.2 

10.4 
8.4 
7.2 
6.5 
5.8 
5.2 
4.5 
3.9 
3.2 

9.8 
7.9 
6.7 
6.2 
5.5 
5.0 
4.3 
3.8 
3.1 

1-9  

1-7  
,    1-6  

1-5  
1-4. 

1-3  

1-2 

1-1  

Relative  Consistency  —  (R)  =  1, 

.10 

1-12  

25.8 
19.9 
16.2 
14.3 
12.3 
10.5 
8.6 
6.6 
4.7 

23.6 
18.4 
14.9 
13.2 
11.4 
9.8 
7.9 
6.3 
4.5 

21.4 
16.7 
13.5 
12.1 
10.5 
9.0 
7.4 
5.9 
4.3 

19.6 
15.4 
12.5 
11.2 
9.8 
8.5 
6.9 
5.6 
4.2 

18.1 
14.2 
11.7 
10.5 
9.1 
7.9 
6.6 
5.4 
4.1 

16.7 
13.2 
10.9 
9.8 
8.6 
7.5 
6.3 
5.2 
4.0 

15.3        14.2- 
12.1        11.2 
10.0         9.5 
9.1         8.5 
8.0         7.6 
6.'9         6.6 
5.9         5.6 
5.0         4.7 
3.9         3.7 

13.2 
10.6 
8.8 
8.0 
7.0 
6.3 
5.4 
4.5 
3.6 

12.2 
9.9 

8.4 
7.5 
6.7 
5.9 
5.1 
4.4 
3.5 

11.4 
9.2 
7.9 

7.2 
6.4 
5.7 
5.0 
4.3 
3.5 

10.8 
8.7 
7.4 
6.8 
6.1 
5.5 
4.7 
4.2 
3.4 

1-9  

1-7 

1-6  

1-5 

1-4.    , 

1-3  

1-2 

1-1  

Relative  Consistency  —  (R)  =  1 

.25 

1-12.  . 

29.4 
22.6 
18.4 
16.3 
14.0 
11.9 
9.8 
7.5 
5.4 

26.8 
20.9 
16.9 
15.0 
13.0 
11.1 
9.0 
7.1 
5.1 

24.4 
19.0 
15.4 
13.8 
11.9 
10.2 
8.4 
6.8 
4.9 

22.2 
17.5 
14.3 
12.8 
11.1 
9.6 
7.9 
6.4 
4.8 

20.5 
16.1 
13.2 
11.9 
10.4 
9.0 
7.5 
6.1 
4.6 

19.0 
15.0 
12.4 
11.1 
9.8 
8.5 
7.1 
5.9 
4.5 

17.4       16.1 
13.8       12.7 
11.4       10.7 
10.4         9.6 
9.1          8.6 
7.9         7.5 
6.8         6.4 
5.6         5.4 
4.4         4.3 

15.0 
12.0 
10.0 
9.1 
8.0 
7.1 
6.1 
5.1 
4.1 

13.9 
11.2 
9.5 
8.5 
7.6 
6.8 
5.8 
5.0 
4.0 

13.0 
10.5 
9.0 
8.1 
7.2 
6.5 
5.6 
4.9 
4.0 

12.3 
9.9 
8.4 
7.7 
6.9 
6.2 
5.4 
4.8 
3.9 

1-9  
1-7  

1-6 

1-5  

1-4  

1-3 

1-2  

1-1  

DESIGN  OF  CONCRETE  MIXTURES 


i 


FIG.   6.     DIAGRAM  FOR  THE  DESIGN  OF  CONCRETE  MIXTURES 
This  chart  is  based  on  compression  tests  of  6  by   12-inch  cylinders;   age  28  days;   stored   in 
damp  sand.     The  cement  used  gave  compressive  strengths  in  1-3  standard  sand  mortar  as  follows: 

Age  Lb.  per  Sq.  In. 

7  days     1,900 

28  days     3,200 

3  months    4,200 

1    year     4,300 


STRUCTURAL  MATERIALS  RESEARCH   LABORATORY 

The  effect  of  using  other  mixes,  gradings  or  consistencies  on  the  strength  can 
be  seen  at  once  from  the  diagram.  For  instance,  if  the  water  were  increased  to  a 
relative  consistency  of  1.25  (not  nearly  so  wet  as  is  frequently  seen  in  road  work) 
the  strength  will  be  reduced  to  2,700  Ib.  per  sq.  in.— a  reduction  of  over  20  per  cent 
If  the  mix  were  changed  to  1 :4y2  and  other  factors  the  same  as  in  the  first  example 
the  strength  would  be  3,200  Ib.  per  sq.  in.  We  should  have  to  change  the  mix  to 
as  lean  as  1 :5*4  in  order  to  secure  the  same  reduction  in  strength  as  was  found 
above  for  a  change  from  1.10  to  1.25  consistency. 

By  using  the  wetter  of  the  two  consistencies  we  secure  concrete  of  the  same 
strength  as  if  we  had  used  one-third  less  cement  and  the  drier  mix.  In  other 
words,  increasing  the  mixing  water  13%  causes  the  same  reduction  in  strength  as 
if  we  should  omit  33%  of  the  cement.  This  example  shows  the  reason  for  empha- 
sizing the  importance  of  proper  control  of  mixing  water  in  concrete. 

This  chart  enables  us  to  answer  such  questions  as  the  following: 

Which  is  the  stronger,  a  1 :3  mortar  or  a  1 :5  concrete  mixture? 

Assuming  that  concrete  of  the  same  plasticity  is  used,  the  relative  strengths  will 
depend,  of  course,  on  the  grading  of  the  aggregates  and  the  mix.  In  one  case  we 
have  assumed  1 :3  mix  with  fineness  modulus  equal  to  3.00.  This  will  give  a  strength 
for  normal  consistency  of  3,000  Ib.  per  sq.  in.  The  1 :5  mix  (fineness  modulus  5.70) 
gives  a  strength  for  normal  consistency  of  about  3,300  Ib.  per  sq.  in.  The  strengths 
for  other  consistencies  can  be  found  by  reading  horizontally  across  the  chart  as  in- 
dicated by  the  dotted  lines. 

Unfortunately,  we  now  have  no  proper  basis  for  absolute  values  for  strength 
of  concrete.  This,  of  course,  makes  it  necessary  to  refer  to  particular  tests  as  in  Fig. 
6.  This  condition  emphasizes  the  importance  of  working  out  a  test  of  cement  which 
will  give  us  at  once  the  concrete  strength  for  given  materials,  mixes,  etc.  With  the 
present  method  of  testing  cement  it  is  impossible  to  do  more  than  make  a  rough 
guess  as  to  the  strength  of  concrete  from  the  results  of  briquet  tests. 

Quantity  of  Water  Required  for  Concrete 

The  formulas  given  above  (4  and  5)  show  the  elements  which  make  up  the  water- 
requirements  of  a  concrete  mix.  Table  5  gives  the  quantity  o£  water  required  for 
certain  mixes  and  values  of  fineness  modulus.  Quantities  are  given  in  terms  of 
gallons  per  sack  of  cement.  In  this  table  the  net  absorption  (that  is,  the  quantity 
of  water  taken  up  by  the  aggregate  in  addition  to  that  already  contained)  is  assumed 
as  0.02  (2%  by  volume).  This  table  is  of  interest  when  we  consider  that  it  has 
been  found  that  a  given  water-ratio  corresponds  to  constant  concrete  strength 
regardless  of  the  combination  of  mix,  consistency  or  grading  of  aggregate  which 
may  be  used,  so  long  as  we  have  a  workable  concrete. 

Further  Discussion  of  Concrete  Mixes 

The  importance  of  the  water-ratio  on  the  strength  of  concrete  will  be  shown  in 
the  following  considerations: 

One  pint  more  water  than  necessary  to  produce  a  plastic  concrete  reduces  the 
strength  to  the  same  extent  as  if  we  should  omit  2  to  3  Ib.  of  cement  from  a  1-bag 
batch. 

Our  studies  give  us  an  entirely  new  conception  of  the  function  performed  by 
the  various  constituent  materials.  The  use  of  a  coarse,  well-graded  aggregate 
results  in  no  gain  in  strength  unless  we  take  advantage  of  the  fact  that  the  amount 
of  water  necessary  to  produce  a  plastic  mix  can  thus  be  reduced.  In  a  similar  way 
we  may  say  that  the  use  of  more  cement  in  a  batch  does  not  produce  any. beneficial 
effect  except  from  the  fact  that  a  plastic,  workable  mix  can  be  produced  with 
a  lower  water-ratio. 

The  reason  a  rich  mixture  gives  a  higher  strength  than  a  lean  one  is  not  that 
more  cement  is  used,  but  because  the  concrete  can  be  mixed  (and  usually  is  mixed) 
with  a  water-ratio  which  is  relatively  lower  for  the  richer  mixtures  than  for  the 
lean  ones.  If  advantage  is  not  taken  of  the  fact  that  in  a  'rich  mix  relatively  less 
water  can  be  used,  no  benefit  will  be  gained  as  compared  with  a  leaner  mix.  In  all 
this  discussion  the  quantity  of  water  is  compared  with  the  quantity  of  cement  in  the 
batch  (cubic  feet  of  water  to  1  sack  of  cement)  and  not  to  the  weight  of  dry 
materials  or  of  the  concrete  as  is  generally  done. 


DESIGN  OF  CONCRETE  MIXTURES 


19 


-|7£fc? 


FIG.    7.      DIAGRAM    FOR    DETERMINING    QUANTITY    OF    SAND    REQUIRED 
IN  CONCRETE  MIXES 


Based  on  equation     p=:100 


A— B 
A— C 


where  p  =  percentage  of  fine  aggregate  in  total  mixture. 
A  ==  fineness  modulus  of  coarse  aggregate. 
B  •=.  fineness  modulus  of  total  aggregate. 
C  =  fineness  modulus  of  fine  aggregate. 


20  STRUCTURAL  MATERIALS  RESEARCH  LABORATORY 

The  mere  use  of  richer  mixes  has  encouraged  a  feeling  of  security,  whereas 
in  many  instances  nothing  more  has  been  accomplished  than  wasting  a  large  quantity 
of  cement,  due  to  the  use  of  an  excess  of  mixing  water.  The  universal  acceptance 
of  this  false  theory  of  concrete  has  exerted  a  most  pernicious  influence  on  the 
proper  use  of  concrete  materials  and  has  proven  to  be  an  almost  insurmountable 
barrier  in  the  way  of  progress  in  the  development  of  sound  principles  of  concrete 
proportioning  and  construction. 

Rich  mixes  and  well-graded  aggregates  are  just  as  essential  as  ever,  but  we 
now  have  a  proper  appreciation  of  the  true  function  of  the  constituent  materials  in 
concrete  and  a  more  thorough  understanding  of  the  injurious  effect  of  too  much 
water.  Rich  mixes  and  well-graded  aggregates  are  after  all  only  a  means  to  an 
end;  that  is,  to  produce  a  plastic,  workable  concrete  with  a  minimum  quantity  of 
water  as  compared  with  the  cement  used.  Workability  of  concrete  mixes  is  of 
fundamental  significance.  This  factor  is  the  only  limitation  which  prevents  the 
reduction  of  cement  and  water  in  the  batch  to  much  lower  limits  than  are  now 
practicable. 

The  above  considerations  show  that  the  water  content  is  the  most  important 
element  of  a  concrete  mix,  in  that  small  variations  in  the  water  cause  a  much  wider 
change  in  the  strength  than  similar  variations  in  the  cement  content  or  the  size  or 
grading  of  the  aggregate.  This  shows  the  absurdity  of  our  present  practice  in 
specifying  definite  gradings  for  aggregates  and  carefully  proportioning  the  cement, 
then  guessing  at  the  water.  It  would  be  more  correct  to  carefully  measure  the 
water  and  guess  at  the  cement  in  the  batch. 

The  grading  of  the  aggregate  may  vary  over  a  wide  range  without  producing 
any  effect  on  concrete  strength,  so  long  as  the  cement  and  water  remain  unchanged. 
The  consistency  of  the  concrete  will  be  changed,  but  this  will  not  affect  the  concrete 
strength  if  all  mixes  are  plastic.  The  possibility  of  improving  the  strength  of 
concrete  by  better  grading  of  aggregates  is  small  as  compared  with  the  advantages 
which  may  be  reaped  from  tasing  as  dry  a  mix  as  can  be  properly  placed.  Table  4 
shows  the  effect  of  water  on  the  strength  of  concrete. 

It  is  impracticable  to  lay  down  a  general  rule  for  the  quantity  of  water  which 
should  be  used  in  a  concrete  mix,  since  it  was  seen  in  the  water  formulas  given 
above  that  the  total  water  is  governed  by  a  large  number  of  different  factors.  How- 
ever, it  is  only  the  water  which  goes  to  the  cement  (that  is,  exclusive  of  absorbed 
water)  which  affects  the  concrete  strength.  The  failure  to  recognize  this  fact  has 
led  to  many  erroneous  conclusions  from  tests  made  to  determine  the  relative  merits 
of  different  aggregates. 

Table  5  gives  the  quantity  of  water  required  for  plastic  mixes  for  certain 
assumed  conditions  of  normal  consistency  of  cement,  absorption  of  aggregate,  and 
relative  consistency.  Water  is  expressed  in  terms  of  gallons  per  sack  of  cement. 
Jn  using  this  table  the  dependence  of  the  value  of  fineness  modulus  which  may  be 
used  on  the  size  of  aggregate  and  the  mix,  referred  to  in  Table  3,  should  not  be 
overlooked. 

Without  regard  to  the  actual  quantity  of  mixing  water,  the  following  rule  is  a 
safe  one  to  follow :  Use  the  smallest  quantity  of  mixing  zvater  that  will  produce  a 
plastic  or  workable  concrete.  The  importance  of  any  method  of  mixing,  handling, 
placing  and  finishing  concrete  which  will  enable  the  builder  to  reduce  the  water 
content  of  the  concrete  to  a  minimum  is  at  once  apparent. 


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